Some things particular to financial systems include internal controls (This is a critical accounting term, do some research to really think this one through). Things like the person entering the check value can't also approve it. Things like using stored procs and not SQL generated from the application so that you can restrict rights to only the procs (no dynamic SQL at all - ever - in a financial system) and so users can only do what they are authorized to do. No rights for anyone except the production dba and an alternate to the tables. Fraud is what you are trying to protect the system from not just outside attacks. Security is critical to financial systems.
You also need audit tables to know who changed what data and when and what the old value was. This is not only an additional way to help find problems if someone got around the internal controls (or the system forgot to implement some critical ones) stole money, but it is often critical to be able to undo a mistake without having to restore. In general accounting systems often have data fields that are not viewable by the user and that are generated through default values or in a way that the user doesn't see them.
Another thing is you need to view actions in time so things that might look like a natural relationship may need denormalizing to preserve what the cost was at the time the action happened. So if you have an hourly rate table, you would use that as a lookup to get the rate at the time of the action not join to it to get the rate when you query.
Financial systems have private data in them, almost always, think how you are going to protect this data. You will need to be encrypting and decrypting data. You probably want an encrypted backup as well.
This data is the lifeblood of a company, it is critical that you have a good backup plan and much practice restoring. Off-site backups are critical.
Data integrity is critical. You need the correct datatypes and you need pk/fk relationships, constraints and triggers to enforce the rules. A fincial system can;t afford to have orphaned records.
You need to consider deletes very carefully. Financial systems often do soft deletes (mark records as deleted to avoid losing historical data. Yes XYZ company is no longer a customer, but you don't want to lose the finacial history of the orders they had in the past. I would not even consider using cascade delete in a financial system.
Don't just talk to accountants in designing the system, talk to financial people who will run the system and auditors who will audit the results. Read and know thoroughly the published accounting standard for the country you are desiging for. Look at tax implications. This is complex stuff.
Think about data warehousing and archiving data. Financial systems often query old data for reports, reporting is big, big, big for financial systems. Think how to do it effectively without affecting day-to-day data entry.